Since the dawn of Seiberg-Witten era [1]}, [2]}, it has been recognized [3]} that there is close connection between 4d \(\mathcal {N}=2\)  systems and completely integrable Hamiltonian systems. In particular, Donagi and Witten [4]} explained that for each 4d \(\mathcal {N}=2\)  supersymmetric field theory there exists a complex integrable systems encoding its Coulomb branch physics. Following [5]} we will call such a complex integrable system a Seiberg-Witten integrable system.
